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Step * 2 1 of Lemma assert-bl-all


1. ∀[T:Type]. ∀[P:T ⟶ 𝔹]. ∀[L:T List].  uiff(↑(∀x∈L.P[x])_b;(∀x∈L.↑P[x]))
2. T : Type
3. L : T List
4. P : {x:T| (x ∈ L)}  ⟶ 𝔹
⊢ uiff(↑(∀x∈L.P[x])_b;(∀x∈L.↑P[x]))
BY
{ (InstHyp [⌜{x:T| (x ∈ L)} ⌝;⌜P⌝;⌜L⌝] 1⋅ THEN Auto) }

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Latex:

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Latex:

1.  \mforall{}[T:Type].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbB{}].  \mforall{}[L:T  List].    uiff(\muparrow{}(\mforall{}x\mmember{}L.P[x])\_b;(\mforall{}x\mmember{}L.\muparrow{}P[x]))
2.  T  :  Type
3.  L  :  T  List
4.  P  :  \{x:T|  (x  \mmember{}  L)\}    {}\mrightarrow{}  \mBbbB{}
\mvdash{}  uiff(\muparrow{}(\mforall{}x\mmember{}L.P[x])\_b;(\mforall{}x\mmember{}L.\muparrow{}P[x]))


By

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Latex:
(InstHyp  [\mkleeneopen{}\{x:T|  (x  \mmember{}  L)\}  \mkleeneclose{};\mkleeneopen{}P\mkleeneclose{};\mkleeneopen{}L\mkleeneclose{}]  1\mcdot{}  THEN  Auto)

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